All our calculations were performed within the DFT scheme, using the projector-augmented plane wave method (PAW) [1]} as implemented in the VASP (version 5.4.4) code [2]}, [3]}. The valence configurations were 4s\(^1\)3d\(^6\) for Mn, and 3s\(^2\)3p\(^4\) for S, respectively. The exchange-correlation (XC) term in the effective Kohn-Sham potential was approximated according to the Perdew-Burke-Ernzerhof parameterization for solids (PBEsol) of the generalized gradient approximation (GGA) [4]}. We also assessed the local density approximation (LDA) [5]} and the standard PBE [6]} XC functionals, but we found that PBEsol produced more accurate structural parameters when compared to available experimental values for both AFM and PM phases of MnS.
Integration in the Brillouin zone was done on a \(\Gamma \) -centered grid of uniformly distributed k-points with a spacing of \(2\pi \times 0.3\)  Å\(^{-1}\) . The selected plane-wave kinetic energy cutoff was 500 eV and convergence of our structural optimizations was assumed when the total energy changes were less than \(10^{-8}\)  eV and the forces on each atom smaller than \(10^{-3}\)  eV/Å.
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